14949 + Interview Questions in Maths in Class 11 Page 119 InterviewSolution

5901.	Write the first four terms of the sequence whose nth term is given (-1)^(n-1) cos "" (npi)/(4)
Answer» ANSWER :`(SQRT(2))/(2),0,(-sqrt(2))/(2) ,1`

Discussion

5902.	Prove that sin^(2)52 1/2-sin^(2)22 1/2.
Answer» `(SQRT(3)+1)/(4sqrt(2))` `(sqrt(3)-1)/(4sqrt(2))` `(3+sqrt(3))/(4sqrt(2))` `(3-sqrt(3))/(4sqrt(2))` ANSWER :A

Discussion

5903.	10 is Geometric mean between 5 and x then x = ......... Where x in R^(+) .
Answer» ANSWER :20

Discussion

5904.	Are the following pair of sets equal? Give reasons A= {x : x is a letter in the word REAP} B= {y : y is a letter in the word ROPE}.
Answer» ANSWER :it is not an EQUAL SET

Discussion

5905.	Find the domains of the following functions f(x) = ( 1)/( sqrt( x^(2) - 4))
Answer» ANSWER :`(-OO,-1) UU ( 1, oo)`

Discussion

5906.	If O is the point inside the triangle ABC such that lfloor OBC = A//2, lfloor OCA = B//2 , lfloor OAB = C//2 then (Sin(A -C//2)Sin(B-C//2).Sin(C-B//2))/(Sin A//2 . Sin B//2.SinC//2) =
Answer» 1 2 3 4 Answer :A

Discussion

5907.	~(p or q)=……
Answer» <P>p and Q `(~p)` and `(~q)` `(~p)` or `(~q)` p or `(~q)` ANSWER :B

Discussion

5908.	Three letters are written to different persons , and the addresses on the three envelopes are also written . Without looking at the addresses , find the probability that the letters go into the right envelopes .
Answer» ANSWER :`(1)/(6)`

Discussion

5909.	Rewrite each of the following statements in the form of conditional statements: You will get a sweet dish after the dinner.
Answer» ANSWER :GET SWEET DISH.

Discussion

5910.	Using binomial theorem, evaluate (99)^5
Answer» ANSWER :9509900499

Discussion

5911.	sin^(2)(51^(@)-x)+sin^(2)(39^(@)+x)=
Answer» -1 0 1 2 Answer :C

Discussion

5912.	Find the points where f(x)={{:(x^(2),x in Q),(2-x^(2),x in Q^(c )):}is continuous on R,
Answer» ANSWER :`-1,1`

Discussion

5913.	Let a_(1) , a_(2) , a_(3) , ..... be terms of an A.P. If (a_(1)+a_(2)+.....+a_(p))/(a_(1)+a_(2)+...... +a_(q))=(p^(2))/(q^(2)) (p ne q) then find (a_(6))/(a_(21)) .
Answer» ANSWER :`(11)/(41)`

Discussion

5914.	IF X and YareindependentbinomialvariablessuchthatX toB(5,0.5) andY to B( 7.0.5).thenp[(X+y) gt 1 ]=….
Answer» `(4095)/(4096)` `(3.9)/(4096)` `(4032)/(4096)` NONEOF these ANSWER :A

Discussion

5915.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Length of perpendicular from origin is 7 unit and slope -1.
Answer» ANSWER :`X + y- 7 SQRT(2) = 0`

Discussion

5916.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Length of perpendicular from origin is 7 unit and makes an angle (pi)/(6) with positive side of X-axis.
Answer» ANSWER :`SQRT(2) x+y = 14`

Discussion

5917.	Evaluate the following limits in lim_(xrarr1)pix^(2)
Answer» ANSWER :`PI`

Discussion

5918.	Find the sum: 1^(1) -2^(2) + 3^(2)-4^(2)+ 5^(2)- 6^(2)+……up to n terms
Answer» ANSWER :`(N(n+1))/(2)`

Discussion

5919.	Range of f(theta) = cos^(2) theta(cos^(2) theta + 1) + 2 sin^(2) theta is
Answer» `[3//4,1]` `[3//16,1]` `[3//4,7//4]` `[7//4,2]` ANSWER :D

Discussion

5920.	Find the sum to8 terms of 3 + 6 + 12 + ...
Answer» ANSWER :765

Discussion

5921.	An open tank is to be constructed with a square base and vertical sides to holda given capacity of water . Theexpense of lining the tank with lead is least when the ratio of the depth and the width is
Answer» `1:1` `1:2` `2:1` `1:3` ANSWER :B

Discussion

5922.	Express the equation 3x^2-y^2=4 of a hyperbola in standard form
Answer» SOLUTION :`x^2/((4/3))-y^2/4=1`

Discussion

5923.	Which of the following sentences are statement ? Justify your answer : (1) sqrt(5) is a rational number. (2)it is a cold day today. (3)The product of 8 and 2 is 16. (4)how many teachers are there in your school ? (5)the sum of interior angles of a quadrilateral is 360^@. (6)go to your room. (7)15 is smaller than 12. (8)there are 7 days in a week. (9)the earth revolves around the sun. (10) 16 has two prime factros. (11) the H.C.F. of 15 and 20 is 16. (12)the L.C.M. of 8 and 12 is 24. (13) the three sides of equilateral triangle are equal. (14) New Delhi is the capital of india. (15) six is a prime number. (16) it was Saturday yesterday. (17) the least natural number is one. (18) maths is an easy subject.
Answer» Solution :(1)`SQRT(5)` is an irrational NUMBER, so the given sentences is false THEREFORE it is a statement. 2. it is not a statement because the w ORD 'taday' is used . (3) it is a statement because sentence is true. (4) it is not a statement because it is a QUESTION. (5) it is a statement because the given sentence is true. (6) it is not a statement because sentence is an order. (7) it is a statement because the given sentence is false. (8) it is a statement because the given sentence is true. (9) it is a statement because the given sentence scientifically true. (10) it is a statement because the given sentence is false. (11) it is a statement because the given sentence is false. (12) it is a statement because the given sentence is true. (13) it is a statement because the given sentence is true. (14) it is a statement because the given sentence is true. (15) it is a statement because the given sentence is false. (16) it is not a statement because the word yesterday 's is used. (17) it is a statement because the given sentence is true. (18) it is not a statement because the given sentence is true for some persons and false for some persons.

Discussion

5924.	The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ……….
Answer» ANSWER :B

Discussion

5925.	Let barb = 2bari + barj - bark, barc = bari + 3bark . If veca is a unit vector then find the maximum value of [bara,barb,barc]
Answer» `-1` `SQRT(10)+SQRT6` `sqrt(59)` `sqrt(60)` Answer :C

Discussion

5926.	Lt_(xto(pi)/(2))(1-sinx)/(cosx) is equal to
Answer» 0 `-1` 1 `1/2` ANSWER :A

Discussion

5927.	Construct a suitable domain X such that f:x to N defined by f (n) = n +3to be one ot one and onto.
Answer» ANSWER :`(-2, 1,0) UU N (or) {-2,-1,0,1,2}`

Discussion

5928.	If P (2,3,1) is a point and L -= x -y -z -2 =0 is a plane then
Answer» origin and P lie on the same SIDE of the plane distance of P from then plane is `(4)/(sqrt3)` foot of perpendicular is `((10)/(3), (5)/(3), -(1)/(3))` image of point P by the plane `((10)/(3), (5)/(3), -(1)/(3))` Answer :A::B::C

Discussion

5929.	The minimum value of the expression sin alpha + sin beta+sin lambda, where alpha,beta,lambda are real numbers satisfying alpha + beta + lambda = pi is
Answer» positive zero negative -3 Answer :C

Discussion

5930.	Find the component statements of the following compound statements: Chennai is in India and it is capital of TamilNadu.
Answer» <P> Answer :p: Chenai is in INDIA. Q: Chennai is the capital of TAMILNADU.

Discussion

5931.	Observe the following list with respect to the line ax+by+c=0 Then the correct answer is
Answer» 1)`{:(A""B""C""D),(3""5""1""2):}` 2)(`{:(A""B""C""D),(3""5""1""4):}` 3)`{:(A""B""C""D),(3""4""1""5):}` 4)`{:(A""B""C""D),(1""2""3""4):}` ANSWER :B

Discussion

5932.	If a, b, c, d are in G.P. then prove that : (i) (a+c)(c+d)=( b+c)(b+d) (ii) (a^(2)+b^(2)+c^(2))(b^(2)+c^(2)+d^(2))=(ab+bc+cd)^(2) (iii) (a+b+c+d)^(2)=(a+b)^(2)+2(b+c)^(2)+(c+d)^(2) (iv) a+b,b+c,c+d" are in G.P." (v) a^(2)+b^(2),b^(2)+c^(2),c^(2)+d^(2)" are in G.P." (vi) a^(n)+b^(n),b^(n)+c^(n),c^(n)+d^(n)" are in G.P."
Answer» SOLUTION :N/a

Discussion

5933.	Write the following in roster form. (i) y=(x+1)^((1/3))(ii) the set of all postive roots of the eqution (x-1)(x+1)(x^(2)-1)=0 (iii) {x in N:4x+9 lt 52}.
Answer» ANSWER :(i) {2,3,5,7} (II) B={1} (iii) A={1,2,3,4,5,6,7,8,9,10} (IV) A={-5}

Discussion

5934.	Find (d )/(dx) [(log x) ^( tan x) ].
Answer» ANSWER :`(TAN X )/( XLOG x)`

Discussion

5935.	Find the roots of quadrratic equation x^2 - 3x +2.
Answer» ANSWER :`=2x-3`

Discussion

5936.	At x=0 f(x) = sinx-x
Answer» Has a minimum Has a maximum Has no extremum Is not defined Answer :C

Discussion

5937.	Find the square roots of the following : 1+4 sqrt(-3)
Answer» ANSWER :`+-(2+sqrt(3)i)`

Discussion

5938.	z and z' are complex numbers such that their product zz' = 3-4i. Given that z' is 5+3i, express z in the form a + bi where a and b are rational numbers.
Answer» ANSWER :`(3)/(34)- (29)/(34)i`

Discussion

5939.	Find thestandard deviation from the followig datas: (a) 10,20,30,40,50,60 (b) 80,85,100,110,82,97,93,95,88,140 (c) 5,15,25,35,40,45,55,60 (d) 4,5,7,4,3,2,4,8,4
Answer» SOLUTION :NA

Discussion

5940.	From the data given below state which group is more variable, A or B?
Answer» ANSWER :B

Discussion

5941.	Let g(x)=1+x-[x] and f(x)= {:{(-1", "x lt 0),(0 ", "x=0),(1", "x gt 0):}. Then for all x, f(g(x)) is equal to ( where [.] represents the greatest integer function)
Answer» x 1 `F(x)` `G(x)` Answer :B

Discussion

5942.	Ifalpha , betaare two different values ofthetalying between0 and2pi which satisfy the equation6 cos theta + 8 sin theta=9, find the value of sin ( alpha + beta).
Answer» ANSWER :`24/25`

Discussion

5943.	Solve: 3x^(2) - 4x + 20/3=0
Answer» ANSWER :`2/3 +- 4/3 i`

Discussion

5944.	Find the sum of the sequence 8, 88, 888, 8888, . . . To n terms.
Answer» ANSWER :`80/81(10^(N)-1)-8/9n`

Discussion

5945.	If the lines 5x - ky +3 = 0and 4x - 3y - 4 = 0are parallel then k = ........... .
Answer» ANSWER :`15/4`

Discussion

5946.	The standard deviation of the data 6,5,9,13,12,8,10 is……..
Answer» `SQRT(52/7)` `52/7` `SQRT6` `6` ANSWER :A

Discussion

5947.	Points (-3, 1, 2), (3, -1, 2) and (-3, 1, -2) are in which octants ?
Answer» ANSWER :II, IV and VI OCTANTS

Discussion

5948.	If there is an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then the percentage error in circumference is
Answer» 0.2 0.02 0.002 0.0002 Answer :A

Discussion

5949.	A point on the line passing through (1, 1, 1) and parallel to (1, -2, -1) is
Answer» (0, 3, 1) (2, 3, 0) (0, 3, 2) (1, 3, 2) ANSWER :C

Discussion

5950.	Given that x in [0,1] andy in [0,1] . LetA bethe eventof (x,y) satisfyingy^(2) le xand B bethe eventsof (x,y) satisfyingx^(2) le y . Then .
Answer» `P( A NN B ) = (1)/(2)` A , Bareexhauive A, B are mutuallyexclusive A, B are independent Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Write the first four terms of the sequence whose nth term is given (-1)^(n-1) cos "" (npi)/(4)

Prove that sin^(2)52 1/2-sin^(2)22 1/2.

10 is Geometric mean between 5 and x then x = ......... Where x in R^(+) .

Are the following pair of sets equal? Give reasons A= {x : x is a letter in the word REAP} B= {y : y is a letter in the word ROPE}.

Find the domains of the following functions f(x) = ( 1)/( sqrt( x^(2) - 4))

If O is the point inside the triangle ABC such that lfloor OBC = A//2, lfloor OCA = B//2 , lfloor OAB = C//2 then (Sin(A -C//2)Sin(B-C//2).Sin(C-B//2))/(Sin A//2 . Sin B//2.SinC//2) =

~(p or q)=……

Three letters are written to different persons , and the addresses on the three envelopes are also written . Without looking at the addresses , find the probability that the letters go into the right envelopes .

Rewrite each of the following statements in the form of conditional statements: You will get a sweet dish after the dinner.

Using binomial theorem, evaluate (99)^5

sin^(2)(51^(@)-x)+sin^(2)(39^(@)+x)=

Find the points where f(x)={{:(x^(2),x in Q),(2-x^(2),x in Q^(c )):}is continuous on R,

Let a_(1) , a_(2) , a_(3) , ..... be terms of an A.P. If (a_(1)+a_(2)+.....+a_(p))/(a_(1)+a_(2)+...... +a_(q))=(p^(2))/(q^(2)) (p ne q) then find (a_(6))/(a_(21)) .

IF X and YareindependentbinomialvariablessuchthatX toB(5,0.5) andY to B( 7.0.5).thenp[(X+y) gt 1 ]=….

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Length of perpendicular from origin is 7 unit and slope -1.

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Length of perpendicular from origin is 7 unit and makes an angle (pi)/(6) with positive side of X-axis.

Evaluate the following limits in lim_(xrarr1)pix^(2)

Find the sum: 1^(1) -2^(2) + 3^(2)-4^(2)+ 5^(2)- 6^(2)+……up to n terms

Range of f(theta) = cos^(2) theta(cos^(2) theta + 1) + 2 sin^(2) theta is

Find the sum to8 terms of 3 + 6 + 12 + ...

An open tank is to be constructed with a square base and vertical sides to holda given capacity of water . Theexpense of lining the tank with lead is least when the ratio of the depth and the width is

Express the equation 3x^2-y^2=4 of a hyperbola in standard form

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ……….

Let barb = 2bari + barj - bark, barc = bari + 3bark . If veca is a unit vector then find the maximum value of [bara,barb,barc]

Lt_(xto(pi)/(2))(1-sinx)/(cosx) is equal to

Construct a suitable domain X such that f:x to N defined by f (n) = n +3to be one ot one and onto.

If P (2,3,1) is a point and L -= x -y -z -2 =0 is a plane then

The minimum value of the expression sin alpha + sin beta+sin lambda, where alpha,beta,lambda are real numbers satisfying alpha + beta + lambda = pi is

Find the component statements of the following compound statements: Chennai is in India and it is capital of TamilNadu.

Observe the following list with respect to the line ax+by+c=0 Then the correct answer is

Write the following in roster form. (i) y=(x+1)^((1/3))(ii) the set of all postive roots of the eqution (x-1)(x+1)(x^(2)-1)=0 (iii) {x in N:4x+9 lt 52}.

Find (d )/(dx) [(log x) ^( tan x) ].

Find the roots of quadrratic equation x^2 - 3x +2.

At x=0 f(x) = sinx-x

Find the square roots of the following : 1+4 sqrt(-3)

z and z' are complex numbers such that their product zz' = 3-4i. Given that z' is 5+3i, express z in the form a + bi where a and b are rational numbers.

Find thestandard deviation from the followig datas: (a) 10,20,30,40,50,60 (b) 80,85,100,110,82,97,93,95,88,140 (c) 5,15,25,35,40,45,55,60 (d) 4,5,7,4,3,2,4,8,4

From the data given below state which group is more variable, A or B?

Let g(x)=1+x-[x] and f(x)= {:{(-1", "x lt 0),(0 ", "x=0),(1", "x gt 0):}. Then for all x, f(g(x)) is equal to ( where [.] represents the greatest integer function)

Ifalpha , betaare two different values ofthetalying between0 and2pi which satisfy the equation6 cos theta + 8 sin theta=9, find the value of sin ( alpha + beta).

Solve: 3x^(2) - 4x + 20/3=0

Find the sum of the sequence 8, 88, 888, 8888, . . . To n terms.

If the lines 5x - ky +3 = 0and 4x - 3y - 4 = 0are parallel then k = ........... .

The standard deviation of the data 6,5,9,13,12,8,10 is……..

Points (-3, 1, 2), (3, -1, 2) and (-3, 1, -2) are in which octants ?

If there is an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then the percentage error in circumference is

A point on the line passing through (1, 1, 1) and parallel to (1, -2, -1) is

Given that x in [0,1] andy in [0,1] . LetA bethe eventof (x,y) satisfyingy^(2) le xand B bethe eventsof (x,y) satisfyingx^(2) le y . Then .